Average Error: 17.9 → 1.7
Time: 17.5s
Precision: 64
\[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
↓
\[\frac{1}{\frac{\frac{t1 + u}{v}}{\frac{-t1}{t1 + u}}}\]
\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}
↓
\frac{1}{\frac{\frac{t1 + u}{v}}{\frac{-t1}{t1 + u}}}
double f(double u, double v, double t1) {
        double r528547 = t1;
        double r528548 = -r528547;
        double r528549 = v;
        double r528550 = r528548 * r528549;
        double r528551 = u;
        double r528552 = r528547 + r528551;
        double r528553 = r528552 * r528552;
        double r528554 = r528550 / r528553;
        return r528554;
}
↓
double f(double u, double v, double t1) {
        double r528555 = 1.0;
        double r528556 = t1;
        double r528557 = u;
        double r528558 = r528556 + r528557;
        double r528559 = v;
        double r528560 = r528558 / r528559;
        double r528561 = -r528556;
        double r528562 = r528561 / r528558;
        double r528563 = r528560 / r528562;
        double r528564 = r528555 / r528563;
        return r528564;
}

Error

Bits error versus u

Bits error versus v

Bits error versus t1

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 17.9

    \[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
  2. Using strategy rm

  3. Applied times-frac1.2

    \[\leadsto \color{blue}{\frac{-t1}{t1 + u} \cdot \frac{v}{t1 + u}}\]
  4. Using strategy rm

  5. Applied associate-*r/1.1

    \[\leadsto \color{blue}{\frac{\frac{-t1}{t1 + u} \cdot v}{t1 + u}}\]
  6. Using strategy rm

  7. Applied associate-/l*1.5

    \[\leadsto \color{blue}{\frac{\frac{-t1}{t1 + u}}{\frac{t1 + u}{v}}}\]
  8. Using strategy rm

  9. Applied clear-num1.7

    \[\leadsto \color{blue}{\frac{1}{\frac{\frac{t1 + u}{v}}{\frac{-t1}{t1 + u}}}}\]

  10. Final simplification1.7

    \[\leadsto \frac{1}{\frac{\frac{t1 + u}{v}}{\frac{-t1}{t1 + u}}}\]

Reproduce

herbie shell --seed 2019155 +o rules:numerics
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))